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© 2015

Multiple Time Scale Dynamics

Textbook

Part of the Applied Mathematical Sciences book series (AMS, volume 191)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Christian Kuehn
    Pages 1-17
  3. Christian Kuehn
    Pages 19-51
  4. Christian Kuehn
    Pages 53-70
  5. Christian Kuehn
    Pages 71-89
  6. Christian Kuehn
    Pages 91-112
  7. Christian Kuehn
    Pages 113-157
  8. Christian Kuehn
    Pages 159-196
  9. Christian Kuehn
    Pages 197-237
  10. Christian Kuehn
    Pages 239-293
  11. Christian Kuehn
    Pages 295-325
  12. Christian Kuehn
    Pages 327-357
  13. Christian Kuehn
    Pages 359-396
  14. Christian Kuehn
    Pages 397-430
  15. Christian Kuehn
    Pages 431-475
  16. Christian Kuehn
    Pages 477-524
  17. Christian Kuehn
    Pages 525-551
  18. Christian Kuehn
    Pages 553-582
  19. Christian Kuehn
    Pages 583-617
  20. Christian Kuehn
    Pages 619-663

About this book

Introduction

This book provides an introduction to dynamical systems with multiple time scales. The approach it takes is to provide an overview of key areas, particularly topics that are less available in the introductory form.  The broad range of topics included makes it accessible for students and researchers new to the field to gain a quick and thorough overview.

The first of its kind, this book merges a wide variety of different mathematical techniques into a more unified framework. The book is highly illustrated with many examples and exercises and an extensive bibliography. The target audience of this  book are senior undergraduates, graduate students as well as researchers interested in using the multiple time scale dynamics theory in nonlinear science, either from a theoretical or a mathematical modeling perspective. 

Keywords

Bifurcations Canards Fast-Slow Systems Geometric Singular Perturbation Theory Invariant Manifolds Mixed-mode Oscillations Multiple Time Scales Normal Hyperbolicity

Authors and affiliations

  1. 1.Institute for Analysis and SC and Scientific ComputingVienna University of TechnologyViennaAustria

About the authors

Christian Kuehn is a Postdoctoral Researcher at Vienna University of Technology, Institute for Analysis and Scientific Computing in Vienna, Austria.  He received his PhD in Applied Mathematics from Cornell University in 2010.  His research areas include: applied mathematics, differential equations, dynamical systems, numerical mathematics, and stochastics.

Bibliographic information

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Reviews

“It merges a wide variety of different mathematical techniques into a more unified framework. … this is a very interesting introduction to multiscale dynamics which will be of much assistance to both students and researchers. The target audience of this book is senior undergraduates and graduate students as well as researchers interested in using the theory of multiple time scale dynamics in nonlinear science, either from a theoretical or a mathematical modeling perspective.” (Tewfik Sari, Mathematical Reviews, May, 2016)

“This interesting monograph is a self-contained, coherent overview of the backgrounds and progress of the dynamical systems with multiple time scales. … The book contains excellent mathematics and is a well-written and unique source of information on the multiple time scale dynamics. I highly recommend it to all researchers and graduate students who would like to understand the geometric singular perturbation theory.” (Robert Vrabel, zbMATH 1335.34001, 2016)